arXiv:2601.14027cs.AI2026-01被引 40

用通用编程代理直接做数学定理证明,无需训练即可提升性能。

Numina-Lean-Agent: An Open and General Agentic Reasoning System for Formal Mathematics

  • 用通用代码代理替代专用证明器,通过替换底座模型实现性能升级。
  • 在普特南2025题上全对(12/12),达到顶尖闭源系统水平。
  • 可与数学家协作形式化复杂定理,适合研究型数学推理场景。

代理系统已成为形式化定理证明的主流范式,通过协调多个模型与工具取得优异表现。但现有方法多依赖任务特定流水线和训练过的形式化证明器,限制了灵活性与可复现性。本文提出直接以通用编程代理作为形式数学推理器的新范式:(1)通用编程代理天然适配多样推理任务;(2)仅需更换底座模型即可提升性能,无需重新训练;(3)MCP支持灵活扩展与自主调用专用工具,避免复杂设计。基于此,我们构建Numina-Lean-Agent,结合Claude Code与Numina-Lean-MCP,实现与Lean的自主交互、相关定理检索、非形式化推导及辅助工具调用。以Claude Opus 4.5为底座模型,该系统在普特南2025竞赛中全部解决(12/12),达到最佳闭源系统水平。此外,我们进一步验证其泛化能力,成功协助数学家形式化布拉姆-李布定理。项目与全部解法已开源:https://github.com/project-numina/numina-lean-agent。

原文摘要 · Abstract (English)

Agentic systems have recently become the dominant paradigm for formal theorem proving, achieving strong performance by coordinating multiple models and tools. However, existing approaches often rely on task-specific pipelines and trained formal provers, limiting their flexibility and reproducibility. In this paper, we propose the paradigm that directly uses a general coding agent as a formal math reasoner. This paradigm is motivated by (1) A general coding agent provides a natural interface for diverse reasoning tasks beyond proving, (2) Performance can be improved by simply replacing the underlying base model, without training, and (3) MCP enables flexible extension and autonomous calling of specialized tools, avoiding complex design. Based on this paradigm, we introduce Numina-Lean-Agent, which combines Claude Code with Numina-Lean-MCP to enable autonomous interaction with Lean, retrieval of relevant theorems, informal proving and auxiliary reasoning tools. Using Claude Opus 4.5 as the base model, Numina-Lean-Agent solves all problems in Putnam 2025 (12 / 12), matching the best closed-source system. Beyond benchmark evaluation, we further demonstrate its generality by interacting with mathematicians to successfully formalize the Brascamp-Lieb theorem. We release Numina-Lean-Agent and all solutions at https://github.com/project-numina/numina-lean-agent.

形式化证明代理系统数学推理

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